Every Roman Numeral sequel (without a 2 or 3 jammed behind it, like X-2 and XIII-2) is its own self contained game, with rare games being tied in loose ways. The worlds are different. The each story doesn't need knowledge of the previous to fully enjoy and the mechanics are so different enough each time that an exert with one game's system may barely understand the next game's. There is no reason why you can't just pick up any in the series and fully understand it as much as a franchise fans who just brought the same game home on launch day and started playing for the first time.
FFXV sound like it plays more like a Kingdom Hearts game than a true Final Fantasy. (And, I wasn't a fan of KH's story, characters, or playstyle, so XV is a hard sell for me.) They are definitely different, but closer than either is to the older FFs. You might want to check out one of the KH titles, too, during the wait for XV.